\(\renewcommand{\hat}[1]{\widehat{#1}}\)

Shared Qs (week_01)


  1. Question

    A lottery offers the following payout scheme:

    profit chance
    -6 0.3
    1 0.4
    2 0.1
    5 0.2

    To analyze this discrete probability distribution, you can use this link:

    https://chadworley.github.io/cltsim.html?poss=-6*1*2*5&wght=0.3*0.4*0.1*0.2

    A friend claims, “I only played that lottery \(n=25\) times, and I’ve won \(\sum x = 35\) dollars.” You wish to judge whether your friend is making an outlandish claim. To do this, you calculate a \(z\) score.

    \[z = \frac{\sum x - n\mu}{\sigma\sqrt{n}}\]

    A typical \(z\) score is between \(-2\) and \(2\) (this happens 95% of the time). A \(z\) score less than \(-3\) or more than \(3\) is quite unlikely (less than 0.3% of the time).

    Is your friend’s claim typical or outlandish? To answer this, calculate a \(z\) score accurate to the hundredths place.

    \[z=\,?\]


    Solution


  2. Question

    A lottery offers the following payout scheme:

    profit chance
    -6 0.4
    0 0.3
    1 0.1
    8 0.2

    To analyze this discrete probability distribution, you can use this link:

    https://chadworley.github.io/cltsim.html?poss=-6*0*1*8&wght=0.4*0.3*0.1*0.2

    A friend claims, “I only played that lottery \(n=25\) times, and I’ve won \(\sum x = 68\) dollars.” You wish to judge whether your friend is making an outlandish claim. To do this, you calculate a \(z\) score.

    \[z = \frac{\sum x - n\mu}{\sigma\sqrt{n}}\]

    A typical \(z\) score is between \(-2\) and \(2\) (this happens 95% of the time). A \(z\) score less than \(-3\) or more than \(3\) is quite unlikely (less than 0.3% of the time).

    Is your friend’s claim typical or outlandish? To answer this, calculate a \(z\) score accurate to the hundredths place.

    \[z=\,?\]


    Solution


  3. Question

    A lottery offers the following payout scheme:

    profit chance
    -7 0.3
    0 0.2
    2 0.4
    9 0.1

    To analyze this discrete probability distribution, you can use this link:

    https://chadworley.github.io/cltsim.html?poss=-7*0*2*9&wght=0.3*0.2*0.4*0.1

    A friend claims, “I only played that lottery \(n=25\) times, and I’ve won \(\sum x = 21\) dollars.” You wish to judge whether your friend is making an outlandish claim. To do this, you calculate a \(z\) score.

    \[z = \frac{\sum x - n\mu}{\sigma\sqrt{n}}\]

    A typical \(z\) score is between \(-2\) and \(2\) (this happens 95% of the time). A \(z\) score less than \(-3\) or more than \(3\) is quite unlikely (less than 0.3% of the time).

    Is your friend’s claim typical or outlandish? To answer this, calculate a \(z\) score accurate to the hundredths place.

    \[z=\,?\]


    Solution


  4. Question

    A lottery offers the following payout scheme:

    profit chance
    -7 0.4
    3 0.2
    4 0.3
    5 0.1

    To analyze this discrete probability distribution, you can use this link:

    https://chadworley.github.io/cltsim.html?poss=-7*3*4*5&wght=0.4*0.2*0.3*0.1

    A friend claims, “I only played that lottery \(n=25\) times, and I’ve won \(\sum x = 24\) dollars.” You wish to judge whether your friend is making an outlandish claim. To do this, you calculate a \(z\) score.

    \[z = \frac{\sum x - n\mu}{\sigma\sqrt{n}}\]

    A typical \(z\) score is between \(-2\) and \(2\) (this happens 95% of the time). A \(z\) score less than \(-3\) or more than \(3\) is quite unlikely (less than 0.3% of the time).

    Is your friend’s claim typical or outlandish? To answer this, calculate a \(z\) score accurate to the hundredths place.

    \[z=\,?\]


    Solution


  5. Question

    A lottery offers the following payout scheme:

    profit chance
    -8 0.4
    2 0.1
    5 0.3
    7 0.2

    To analyze this discrete probability distribution, you can use this link:

    https://chadworley.github.io/cltsim.html?poss=-8*2*5*7&wght=0.4*0.1*0.3*0.2

    A friend claims, “I only played that lottery \(n=25\) times, and I’ve won \(\sum x = 113\) dollars.” You wish to judge whether your friend is making an outlandish claim. To do this, you calculate a \(z\) score.

    \[z = \frac{\sum x - n\mu}{\sigma\sqrt{n}}\]

    A typical \(z\) score is between \(-2\) and \(2\) (this happens 95% of the time). A \(z\) score less than \(-3\) or more than \(3\) is quite unlikely (less than 0.3% of the time).

    Is your friend’s claim typical or outlandish? To answer this, calculate a \(z\) score accurate to the hundredths place.

    \[z=\,?\]


    Solution


  6. Question

    A lottery offers the following payout scheme:

    profit chance
    -5 0.3
    0 0.4
    2 0.2
    4 0.1

    To analyze this discrete probability distribution, you can use this link:

    https://chadworley.github.io/cltsim.html?poss=-5*0*2*4&wght=0.3*0.4*0.2*0.1

    A friend claims, “I only played that lottery \(n=25\) times, and I’ve won \(\sum x = 29\) dollars.” You wish to judge whether your friend is making an outlandish claim. To do this, you calculate a \(z\) score.

    \[z = \frac{\sum x - n\mu}{\sigma\sqrt{n}}\]

    A typical \(z\) score is between \(-2\) and \(2\) (this happens 95% of the time). A \(z\) score less than \(-3\) or more than \(3\) is quite unlikely (less than 0.3% of the time).

    Is your friend’s claim typical or outlandish? To answer this, calculate a \(z\) score accurate to the hundredths place.

    \[z=\,?\]


    Solution


  7. Question

    A lottery offers the following payout scheme:

    profit chance
    -7 0.3
    1 0.4
    3 0.1
    6 0.2

    To analyze this discrete probability distribution, you can use this link:

    https://chadworley.github.io/cltsim.html?poss=-7*1*3*6&wght=0.3*0.4*0.1*0.2

    A friend claims, “I only played that lottery \(n=25\) times, and I’ve won \(\sum x = 24\) dollars.” You wish to judge whether your friend is making an outlandish claim. To do this, you calculate a \(z\) score.

    \[z = \frac{\sum x - n\mu}{\sigma\sqrt{n}}\]

    A typical \(z\) score is between \(-2\) and \(2\) (this happens 95% of the time). A \(z\) score less than \(-3\) or more than \(3\) is quite unlikely (less than 0.3% of the time).

    Is your friend’s claim typical or outlandish? To answer this, calculate a \(z\) score accurate to the hundredths place.

    \[z=\,?\]


    Solution


  8. Question

    A lottery offers the following payout scheme:

    profit chance
    -6 0.3
    0 0.4
    5 0.2
    7 0.1

    To analyze this discrete probability distribution, you can use this link:

    https://chadworley.github.io/cltsim.html?poss=-6*0*5*7&wght=0.3*0.4*0.2*0.1

    A friend claims, “I only played that lottery \(n=25\) times, and I’ve won \(\sum x = 75\) dollars.” You wish to judge whether your friend is making an outlandish claim. To do this, you calculate a \(z\) score.

    \[z = \frac{\sum x - n\mu}{\sigma\sqrt{n}}\]

    A typical \(z\) score is between \(-2\) and \(2\) (this happens 95% of the time). A \(z\) score less than \(-3\) or more than \(3\) is quite unlikely (less than 0.3% of the time).

    Is your friend’s claim typical or outlandish? To answer this, calculate a \(z\) score accurate to the hundredths place.

    \[z=\,?\]


    Solution


  9. Question

    A lottery offers the following payout scheme:

    profit chance
    -7 0.4
    1 0.3
    5 0.1
    6 0.2

    To analyze this discrete probability distribution, you can use this link:

    https://chadworley.github.io/cltsim.html?poss=-7*1*5*6&wght=0.4*0.3*0.1*0.2

    A friend claims, “I only played that lottery \(n=25\) times, and I’ve won \(\sum x = 66\) dollars.” You wish to judge whether your friend is making an outlandish claim. To do this, you calculate a \(z\) score.

    \[z = \frac{\sum x - n\mu}{\sigma\sqrt{n}}\]

    A typical \(z\) score is between \(-2\) and \(2\) (this happens 95% of the time). A \(z\) score less than \(-3\) or more than \(3\) is quite unlikely (less than 0.3% of the time).

    Is your friend’s claim typical or outlandish? To answer this, calculate a \(z\) score accurate to the hundredths place.

    \[z=\,?\]


    Solution


  10. Question

    A lottery offers the following payout scheme:

    profit chance
    -8 0.3
    0 0.1
    2 0.4
    6 0.2

    To analyze this discrete probability distribution, you can use this link:

    https://chadworley.github.io/cltsim.html?poss=-8*0*2*6&wght=0.3*0.1*0.4*0.2

    A friend claims, “I only played that lottery \(n=25\) times, and I’ve won \(\sum x = 36\) dollars.” You wish to judge whether your friend is making an outlandish claim. To do this, you calculate a \(z\) score.

    \[z = \frac{\sum x - n\mu}{\sigma\sqrt{n}}\]

    A typical \(z\) score is between \(-2\) and \(2\) (this happens 95% of the time). A \(z\) score less than \(-3\) or more than \(3\) is quite unlikely (less than 0.3% of the time).

    Is your friend’s claim typical or outlandish? To answer this, calculate a \(z\) score accurate to the hundredths place.

    \[z=\,?\]


    Solution


  11. Question

    A lottery offers the following payout scheme:

    profit chance
    -8 0.3
    0 0.2
    2 0.4
    3 0.1

    Calculate \(\mu\), the population mean.

    \[\mu = \sum x_i \cdot p_i\]

    This formula tells you to multiply each profit by its chance, and then add up all those products.


    Solution


  12. Question

    A lottery offers the following payout scheme:

    profit chance
    -6 0.4
    0 0.3
    1 0.2
    8 0.1

    Calculate \(\mu\), the population mean.

    \[\mu = \sum x_i \cdot p_i\]

    This formula tells you to multiply each profit by its chance, and then add up all those products.


    Solution


  13. Question

    A lottery offers the following payout scheme:

    profit chance
    -9 0.3
    1 0.1
    3 0.4
    5 0.2

    Calculate \(\mu\), the population mean.

    \[\mu = \sum x_i \cdot p_i\]

    This formula tells you to multiply each profit by its chance, and then add up all those products.


    Solution


  14. Question

    A lottery offers the following payout scheme:

    profit chance
    -4 0.4
    1 0.3
    2 0.2
    3 0.1

    Calculate \(\mu\), the population mean.

    \[\mu = \sum x_i \cdot p_i\]

    This formula tells you to multiply each profit by its chance, and then add up all those products.


    Solution


  15. Question

    A lottery offers the following payout scheme:

    profit chance
    -9 0.4
    2 0.1
    5 0.3
    8 0.2

    Calculate \(\mu\), the population mean.

    \[\mu = \sum x_i \cdot p_i\]

    This formula tells you to multiply each profit by its chance, and then add up all those products.


    Solution


  16. Question

    A lottery offers the following payout scheme:

    profit chance
    -9 0.2
    0 0.4
    3 0.3
    5 0.1

    Calculate \(\mu\), the population mean.

    \[\mu = \sum x_i \cdot p_i\]

    This formula tells you to multiply each profit by its chance, and then add up all those products.


    Solution


  17. Question

    A lottery offers the following payout scheme:

    profit chance
    -7 0.3
    1 0.4
    4 0.1
    6 0.2

    Calculate \(\mu\), the population mean.

    \[\mu = \sum x_i \cdot p_i\]

    This formula tells you to multiply each profit by its chance, and then add up all those products.


    Solution


  18. Question

    A lottery offers the following payout scheme:

    profit chance
    -8 0.3
    1 0.4
    2 0.2
    3 0.1

    Calculate \(\mu\), the population mean.

    \[\mu = \sum x_i \cdot p_i\]

    This formula tells you to multiply each profit by its chance, and then add up all those products.


    Solution


  19. Question

    A lottery offers the following payout scheme:

    profit chance
    -8 0.4
    1 0.2
    5 0.1
    6 0.3

    Calculate \(\mu\), the population mean.

    \[\mu = \sum x_i \cdot p_i\]

    This formula tells you to multiply each profit by its chance, and then add up all those products.


    Solution


  20. Question

    A lottery offers the following payout scheme:

    profit chance
    -6 0.4
    0 0.3
    1 0.1
    3 0.2

    Calculate \(\mu\), the population mean.

    \[\mu = \sum x_i \cdot p_i\]

    This formula tells you to multiply each profit by its chance, and then add up all those products.


    Solution


  21. Question

    Determine the probability that the standard normal variable is less than -0.62. In other words, evaluate \(P(Z < -0.62)\).


    Solution


  22. Question

    Determine the probability that the standard normal variable is less than -1.05. In other words, evaluate \(P(Z < -1.05)\).


    Solution


  23. Question

    Determine the probability that the standard normal variable is less than 0.51. In other words, evaluate \(P(Z < 0.51)\).


    Solution


  24. Question

    Determine the probability that the standard normal variable is less than 0.36. In other words, evaluate \(P(Z < 0.36)\).


    Solution


  25. Question

    Determine the probability that the standard normal variable is less than -0.54. In other words, evaluate \(P(Z < -0.54)\).


    Solution


  26. Question

    Determine the probability that the standard normal variable is less than 0.58. In other words, evaluate \(P(Z < 0.58)\).


    Solution


  27. Question

    Determine the probability that the standard normal variable is less than -0.59. In other words, evaluate \(P(Z < -0.59)\).


    Solution


  28. Question

    Determine the probability that the standard normal variable is less than 1.76. In other words, evaluate \(P(Z < 1.76)\).


    Solution


  29. Question

    Determine the probability that the standard normal variable is less than 0.99. In other words, evaluate \(P(Z < 0.99)\).


    Solution


  30. Question

    Determine the probability that the standard normal variable is less than 0.77. In other words, evaluate \(P(Z < 0.77)\).


    Solution


  31. Question

    Determine the probability that the standard normal variable is more than -1.36. In other words, evaluate \(P(Z > -1.36)\).


    Solution


  32. Question

    Determine the probability that the standard normal variable is more than -1. In other words, evaluate \(P(Z > -1)\).


    Solution


  33. Question

    Determine the probability that the standard normal variable is more than -0.23. In other words, evaluate \(P(Z > -0.23)\).


    Solution


  34. Question

    Determine the probability that the standard normal variable is more than 0.84. In other words, evaluate \(P(Z > 0.84)\).


    Solution


  35. Question

    Determine the probability that the standard normal variable is more than 0.26. In other words, evaluate \(P(Z > 0.26)\).


    Solution


  36. Question

    Determine the probability that the standard normal variable is more than 0.63. In other words, evaluate \(P(Z > 0.63)\).


    Solution


  37. Question

    Determine the probability that the standard normal variable is more than 0.93. In other words, evaluate \(P(Z > 0.93)\).


    Solution


  38. Question

    Determine the probability that the standard normal variable is more than -0.6. In other words, evaluate \(P(Z > -0.6)\).


    Solution


  39. Question

    Determine the probability that the standard normal variable is more than -0.64. In other words, evaluate \(P(Z > -0.64)\).


    Solution


  40. Question

    Determine the probability that the standard normal variable is more than -0.81. In other words, evaluate \(P(Z > -0.81)\).


    Solution


  41. Question

    Determine the probability that the absolute standard normal variable is less than 0.68. In other words, evaluate \(P\left(|Z| < 0.68\right)\).


    Solution


  42. Question

    Determine the probability that the absolute standard normal variable is less than 1.04. In other words, evaluate \(P\left(|Z| < 1.04\right)\).


    Solution


  43. Question

    Determine the probability that the absolute standard normal variable is less than 0.69. In other words, evaluate \(P\left(|Z| < 0.69\right)\).


    Solution


  44. Question

    Determine the probability that the absolute standard normal variable is less than 0.96. In other words, evaluate \(P\left(|Z| < 0.96\right)\).


    Solution


  45. Question

    Determine the probability that the absolute standard normal variable is less than 0.57. In other words, evaluate \(P\left(|Z| < 0.57\right)\).


    Solution


  46. Question

    Determine the probability that the absolute standard normal variable is less than 1.29. In other words, evaluate \(P\left(|Z| < 1.29\right)\).


    Solution


  47. Question

    Determine the probability that the absolute standard normal variable is less than 1.1. In other words, evaluate \(P\left(|Z| < 1.1\right)\).


    Solution


  48. Question

    Determine the probability that the absolute standard normal variable is less than 1.32. In other words, evaluate \(P\left(|Z| < 1.32\right)\).


    Solution


  49. Question

    Determine the probability that the absolute standard normal variable is less than 0.62. In other words, evaluate \(P\left(|Z| < 0.62\right)\).


    Solution


  50. Question

    Determine the probability that the absolute standard normal variable is less than 0.44. In other words, evaluate \(P\left(|Z| < 0.44\right)\).


    Solution


  51. Question

    Determine the probability that the absolute standard normal variable is more than 0.57. In other words, evaluate \(P\left(|Z| > 0.57\right)\).


    Solution


  52. Question

    Determine the probability that the absolute standard normal variable is more than 0.85. In other words, evaluate \(P\left(|Z| > 0.85\right)\).


    Solution


  53. Question

    Determine the probability that the absolute standard normal variable is more than 1.12. In other words, evaluate \(P\left(|Z| > 1.12\right)\).


    Solution


  54. Question

    Determine the probability that the absolute standard normal variable is more than 1.75. In other words, evaluate \(P\left(|Z| > 1.75\right)\).


    Solution


  55. Question

    Determine the probability that the absolute standard normal variable is more than 1.7. In other words, evaluate \(P\left(|Z| > 1.7\right)\).


    Solution


  56. Question

    Determine the probability that the absolute standard normal variable is more than 0.99. In other words, evaluate \(P\left(|Z| > 0.99\right)\).


    Solution


  57. Question

    Determine the probability that the absolute standard normal variable is more than 0.83. In other words, evaluate \(P\left(|Z| > 0.83\right)\).


    Solution


  58. Question

    Determine the probability that the absolute standard normal variable is more than 1.8. In other words, evaluate \(P\left(|Z| > 1.8\right)\).


    Solution


  59. Question

    Determine the probability that the absolute standard normal variable is more than 0.88. In other words, evaluate \(P\left(|Z| > 0.88\right)\).


    Solution


  60. Question

    Determine the probability that the absolute standard normal variable is more than 0.48. In other words, evaluate \(P\left(|Z| > 0.48\right)\).


    Solution


  61. Question

    Determine the probability that the standard normal variable is between -1.54 and 0.09. In other words, evaluate \(P(-1.54 < Z < 0.09)\).


    Solution


  62. Question

    Determine the probability that the standard normal variable is between -0.56 and 0.52. In other words, evaluate \(P(-0.56 < Z < 0.52)\).


    Solution


  63. Question

    Determine the probability that the standard normal variable is between -0.99 and 0.08. In other words, evaluate \(P(-0.99 < Z < 0.08)\).


    Solution


  64. Question

    Determine the probability that the standard normal variable is between -0.28 and 0.7. In other words, evaluate \(P(-0.28 < Z < 0.7)\).


    Solution


  65. Question

    Determine the probability that the standard normal variable is between 0.22 and 1.88. In other words, evaluate \(P(0.22 < Z < 1.88)\).


    Solution


  66. Question

    Determine the probability that the standard normal variable is between -1.6 and 1.09. In other words, evaluate \(P(-1.6 < Z < 1.09)\).


    Solution


  67. Question

    Determine the probability that the standard normal variable is between -0.08 and 0.51. In other words, evaluate \(P(-0.08 < Z < 0.51)\).


    Solution


  68. Question

    Determine the probability that the standard normal variable is between -1.06 and 0. In other words, evaluate \(P(-1.06 < Z < 0)\).


    Solution


  69. Question

    Determine the probability that the standard normal variable is between 0.34 and 1.98. In other words, evaluate \(P(0.34 < Z < 1.98)\).


    Solution


  70. Question

    Determine the probability that the standard normal variable is between -1.15 and 1.45. In other words, evaluate \(P(-1.15 < Z < 1.45)\).


    Solution


  71. Question

    Determine \(z\) such that \(P(Z<z)=0.82\). In other words, what \(z\)-score is greater than \(82\)% of standard normal values? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  72. Question

    Determine \(z\) such that \(P(Z<z)=0.45\). In other words, what \(z\)-score is greater than \(45\)% of standard normal values? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  73. Question

    Determine \(z\) such that \(P(Z<z)=0.52\). In other words, what \(z\)-score is greater than \(52\)% of standard normal values? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  74. Question

    Determine \(z\) such that \(P(Z<z)=0.41\). In other words, what \(z\)-score is greater than \(41\)% of standard normal values? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  75. Question

    Determine \(z\) such that \(P(Z<z)=0.25\). In other words, what \(z\)-score is greater than \(25\)% of standard normal values? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  76. Question

    Determine \(z\) such that \(P(Z<z)=0.75\). In other words, what \(z\)-score is greater than \(75\)% of standard normal values? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  77. Question

    Determine \(z\) such that \(P(Z<z)=0.28\). In other words, what \(z\)-score is greater than \(28\)% of standard normal values? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  78. Question

    Determine \(z\) such that \(P(Z<z)=0.15\). In other words, what \(z\)-score is greater than \(15\)% of standard normal values? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  79. Question

    Determine \(z\) such that \(P(Z<z)=0.32\). In other words, what \(z\)-score is greater than \(32\)% of standard normal values? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  80. Question

    Determine \(z\) such that \(P(Z<z)=0.85\). In other words, what \(z\)-score is greater than \(85\)% of standard normal values? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  81. Question

    Determine \(z\) such that \(P(Z>z)=0.36\). In other words, what \(z\)-score is less than \(36\)% of standard normal values? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  82. Question

    Determine \(z\) such that \(P(Z>z)=0.9\). In other words, what \(z\)-score is less than \(90\)% of standard normal values? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  83. Question

    Determine \(z\) such that \(P(Z>z)=0.73\). In other words, what \(z\)-score is less than \(73\)% of standard normal values? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  84. Question

    Determine \(z\) such that \(P(Z>z)=0.89\). In other words, what \(z\)-score is less than \(89\)% of standard normal values? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  85. Question

    Determine \(z\) such that \(P(Z>z)=0.9\). In other words, what \(z\)-score is less than \(90\)% of standard normal values? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  86. Question

    Determine \(z\) such that \(P(Z>z)=0.32\). In other words, what \(z\)-score is less than \(32\)% of standard normal values? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  87. Question

    Determine \(z\) such that \(P(Z>z)=0.79\). In other words, what \(z\)-score is less than \(79\)% of standard normal values? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  88. Question

    Determine \(z\) such that \(P(Z>z)=0.76\). In other words, what \(z\)-score is less than \(76\)% of standard normal values? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  89. Question

    Determine \(z\) such that \(P(Z>z)=0.19\). In other words, what \(z\)-score is less than \(19\)% of standard normal values? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  90. Question

    Determine \(z\) such that \(P(Z>z)=0.46\). In other words, what \(z\)-score is less than \(46\)% of standard normal values? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  91. Question

    Determine \(z\) such that \(P(|Z|<z)=0.38\). In other words, how far from 0 should boundaries be set such that 38% of standard normal values are between those boundaries? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  92. Question

    Determine \(z\) such that \(P(|Z|<z)=0.38\). In other words, how far from 0 should boundaries be set such that 38% of standard normal values are between those boundaries? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  93. Question

    Determine \(z\) such that \(P(|Z|<z)=0.96\). In other words, how far from 0 should boundaries be set such that 96% of standard normal values are between those boundaries? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  94. Question

    Determine \(z\) such that \(P(|Z|<z)=0.54\). In other words, how far from 0 should boundaries be set such that 54% of standard normal values are between those boundaries? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  95. Question

    Determine \(z\) such that \(P(|Z|<z)=0.24\). In other words, how far from 0 should boundaries be set such that 24% of standard normal values are between those boundaries? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  96. Question

    Determine \(z\) such that \(P(|Z|<z)=0.36\). In other words, how far from 0 should boundaries be set such that 36% of standard normal values are between those boundaries? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  97. Question

    Determine \(z\) such that \(P(|Z|<z)=0.96\). In other words, how far from 0 should boundaries be set such that 96% of standard normal values are between those boundaries? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  98. Question

    Determine \(z\) such that \(P(|Z|<z)=0.9\). In other words, how far from 0 should boundaries be set such that 90% of standard normal values are between those boundaries? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  99. Question

    Determine \(z\) such that \(P(|Z|<z)=0.62\). In other words, how far from 0 should boundaries be set such that 62% of standard normal values are between those boundaries? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  100. Question

    Determine \(z\) such that \(P(|Z|<z)=0.76\). In other words, how far from 0 should boundaries be set such that 76% of standard normal values are between those boundaries? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  101. Question

    Determine \(z\) such that \(P(|Z|>z)=0.06\). In other words, how far from 0 should boundaries be set such that 6% of standard normal values are outside those boundaries? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  102. Question

    Determine \(z\) such that \(P(|Z|>z)=0.38\). In other words, how far from 0 should boundaries be set such that 38% of standard normal values are outside those boundaries? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  103. Question

    Determine \(z\) such that \(P(|Z|>z)=0.5\). In other words, how far from 0 should boundaries be set such that 50% of standard normal values are outside those boundaries? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  104. Question

    Determine \(z\) such that \(P(|Z|>z)=0.58\). In other words, how far from 0 should boundaries be set such that 58% of standard normal values are outside those boundaries? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  105. Question

    Determine \(z\) such that \(P(|Z|>z)=0.42\). In other words, how far from 0 should boundaries be set such that 42% of standard normal values are outside those boundaries? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  106. Question

    Determine \(z\) such that \(P(|Z|>z)=0.4\). In other words, how far from 0 should boundaries be set such that 40% of standard normal values are outside those boundaries? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  107. Question

    Determine \(z\) such that \(P(|Z|>z)=0.66\). In other words, how far from 0 should boundaries be set such that 66% of standard normal values are outside those boundaries? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  108. Question

    Determine \(z\) such that \(P(|Z|>z)=0.74\). In other words, how far from 0 should boundaries be set such that 74% of standard normal values are outside those boundaries? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  109. Question

    Determine \(z\) such that \(P(|Z|>z)=0.14\). In other words, how far from 0 should boundaries be set such that 14% of standard normal values are outside those boundaries? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  110. Question

    Determine \(z\) such that \(P(|Z|>z)=0.1\). In other words, how far from 0 should boundaries be set such that 10% of standard normal values are outside those boundaries? (Answers within 0.01 from the correct value will be marked correct.)


    Solution


  111. Question

    A scientist is investigating whether a chemical may effect the growth of an organism. Under the control conditions (no chemical), the organism grows to a mean mass of \(\mu_0 = 14\) grams with a standard deviation of \(\sigma_0 =3.9\) grams. These population parameters are known precisely because the organism has been grown under control conditions many many times.

    The scientist has only grown the organism under experimental conditions (with chemical) \(n=37\) times. In that sample, the masses have a mean \(\bar{x}=12.68\).

    The scientist wonders if this sample mean is significantly different from \(\mu_0\). To investigate this, the scientist will determine the \(p\)-value. The \(p\)-value represents the probability of getting a sample mean as far (or farther) from \(\mu_0\) due to chance alone.

    It is common to compare the \(p\)-value to 0.05.

    \[p\text{-value} ~=~ P\left(\big|Z\big| > \frac{\big|\bar{x}-\mu_0\big|}{\sigma_0/\sqrt{n}} \right) \]

    Determine the \(p\)-value.


    Solution


  112. Question

    A scientist is investigating whether a chemical may effect the growth of an organism. Under the control conditions (no chemical), the organism grows to a mean mass of \(\mu_0 = 63.6\) grams with a standard deviation of \(\sigma_0 =19\) grams. These population parameters are known precisely because the organism has been grown under control conditions many many times.

    The scientist has only grown the organism under experimental conditions (with chemical) \(n=79\) times. In that sample, the masses have a mean \(\bar{x}=58.43\).

    The scientist wonders if this sample mean is significantly different from \(\mu_0\). To investigate this, the scientist will determine the \(p\)-value. The \(p\)-value represents the probability of getting a sample mean as far (or farther) from \(\mu_0\) due to chance alone.

    It is common to compare the \(p\)-value to 0.05.

    \[p\text{-value} ~=~ P\left(\big|Z\big| > \frac{\big|\bar{x}-\mu_0\big|}{\sigma_0/\sqrt{n}} \right) \]

    Determine the \(p\)-value.


    Solution


  113. Question

    A scientist is investigating whether a chemical may effect the growth of an organism. Under the control conditions (no chemical), the organism grows to a mean mass of \(\mu_0 = 16.5\) grams with a standard deviation of \(\sigma_0 =5.4\) grams. These population parameters are known precisely because the organism has been grown under control conditions many many times.

    The scientist has only grown the organism under experimental conditions (with chemical) \(n=88\) times. In that sample, the masses have a mean \(\bar{x}=15.14\).

    The scientist wonders if this sample mean is significantly different from \(\mu_0\). To investigate this, the scientist will determine the \(p\)-value. The \(p\)-value represents the probability of getting a sample mean as far (or farther) from \(\mu_0\) due to chance alone.

    It is common to compare the \(p\)-value to 0.05.

    \[p\text{-value} ~=~ P\left(\big|Z\big| > \frac{\big|\bar{x}-\mu_0\big|}{\sigma_0/\sqrt{n}} \right) \]

    Determine the \(p\)-value.


    Solution


  114. Question

    A scientist is investigating whether a chemical may effect the growth of an organism. Under the control conditions (no chemical), the organism grows to a mean mass of \(\mu_0 = 31.7\) grams with a standard deviation of \(\sigma_0 =8.2\) grams. These population parameters are known precisely because the organism has been grown under control conditions many many times.

    The scientist has only grown the organism under experimental conditions (with chemical) \(n=30\) times. In that sample, the masses have a mean \(\bar{x}=28.39\).

    The scientist wonders if this sample mean is significantly different from \(\mu_0\). To investigate this, the scientist will determine the \(p\)-value. The \(p\)-value represents the probability of getting a sample mean as far (or farther) from \(\mu_0\) due to chance alone.

    It is common to compare the \(p\)-value to 0.05.

    \[p\text{-value} ~=~ P\left(\big|Z\big| > \frac{\big|\bar{x}-\mu_0\big|}{\sigma_0/\sqrt{n}} \right) \]

    Determine the \(p\)-value.


    Solution


  115. Question

    A scientist is investigating whether a chemical may effect the growth of an organism. Under the control conditions (no chemical), the organism grows to a mean mass of \(\mu_0 = 79.4\) grams with a standard deviation of \(\sigma_0 =22.5\) grams. These population parameters are known precisely because the organism has been grown under control conditions many many times.

    The scientist has only grown the organism under experimental conditions (with chemical) \(n=71\) times. In that sample, the masses have a mean \(\bar{x}=85.22\).

    The scientist wonders if this sample mean is significantly different from \(\mu_0\). To investigate this, the scientist will determine the \(p\)-value. The \(p\)-value represents the probability of getting a sample mean as far (or farther) from \(\mu_0\) due to chance alone.

    It is common to compare the \(p\)-value to 0.05.

    \[p\text{-value} ~=~ P\left(\big|Z\big| > \frac{\big|\bar{x}-\mu_0\big|}{\sigma_0/\sqrt{n}} \right) \]

    Determine the \(p\)-value.


    Solution


  116. Question

    A scientist is investigating whether a chemical may effect the growth of an organism. Under the control conditions (no chemical), the organism grows to a mean mass of \(\mu_0 = 59.3\) grams with a standard deviation of \(\sigma_0 =10.5\) grams. These population parameters are known precisely because the organism has been grown under control conditions many many times.

    The scientist has only grown the organism under experimental conditions (with chemical) \(n=65\) times. In that sample, the masses have a mean \(\bar{x}=56.97\).

    The scientist wonders if this sample mean is significantly different from \(\mu_0\). To investigate this, the scientist will determine the \(p\)-value. The \(p\)-value represents the probability of getting a sample mean as far (or farther) from \(\mu_0\) due to chance alone.

    It is common to compare the \(p\)-value to 0.05.

    \[p\text{-value} ~=~ P\left(\big|Z\big| > \frac{\big|\bar{x}-\mu_0\big|}{\sigma_0/\sqrt{n}} \right) \]

    Determine the \(p\)-value.


    Solution


  117. Question

    A scientist is investigating whether a chemical may effect the growth of an organism. Under the control conditions (no chemical), the organism grows to a mean mass of \(\mu_0 = 87.9\) grams with a standard deviation of \(\sigma_0 =15.9\) grams. These population parameters are known precisely because the organism has been grown under control conditions many many times.

    The scientist has only grown the organism under experimental conditions (with chemical) \(n=67\) times. In that sample, the masses have a mean \(\bar{x}=84.46\).

    The scientist wonders if this sample mean is significantly different from \(\mu_0\). To investigate this, the scientist will determine the \(p\)-value. The \(p\)-value represents the probability of getting a sample mean as far (or farther) from \(\mu_0\) due to chance alone.

    It is common to compare the \(p\)-value to 0.05.

    \[p\text{-value} ~=~ P\left(\big|Z\big| > \frac{\big|\bar{x}-\mu_0\big|}{\sigma_0/\sqrt{n}} \right) \]

    Determine the \(p\)-value.


    Solution


  118. Question

    A scientist is investigating whether a chemical may effect the growth of an organism. Under the control conditions (no chemical), the organism grows to a mean mass of \(\mu_0 = 13.3\) grams with a standard deviation of \(\sigma_0 =3\) grams. These population parameters are known precisely because the organism has been grown under control conditions many many times.

    The scientist has only grown the organism under experimental conditions (with chemical) \(n=88\) times. In that sample, the masses have a mean \(\bar{x}=13.85\).

    The scientist wonders if this sample mean is significantly different from \(\mu_0\). To investigate this, the scientist will determine the \(p\)-value. The \(p\)-value represents the probability of getting a sample mean as far (or farther) from \(\mu_0\) due to chance alone.

    It is common to compare the \(p\)-value to 0.05.

    \[p\text{-value} ~=~ P\left(\big|Z\big| > \frac{\big|\bar{x}-\mu_0\big|}{\sigma_0/\sqrt{n}} \right) \]

    Determine the \(p\)-value.


    Solution


  119. Question

    A scientist is investigating whether a chemical may effect the growth of an organism. Under the control conditions (no chemical), the organism grows to a mean mass of \(\mu_0 = 36.2\) grams with a standard deviation of \(\sigma_0 =9.8\) grams. These population parameters are known precisely because the organism has been grown under control conditions many many times.

    The scientist has only grown the organism under experimental conditions (with chemical) \(n=74\) times. In that sample, the masses have a mean \(\bar{x}=34.16\).

    The scientist wonders if this sample mean is significantly different from \(\mu_0\). To investigate this, the scientist will determine the \(p\)-value. The \(p\)-value represents the probability of getting a sample mean as far (or farther) from \(\mu_0\) due to chance alone.

    It is common to compare the \(p\)-value to 0.05.

    \[p\text{-value} ~=~ P\left(\big|Z\big| > \frac{\big|\bar{x}-\mu_0\big|}{\sigma_0/\sqrt{n}} \right) \]

    Determine the \(p\)-value.


    Solution


  120. Question

    A scientist is investigating whether a chemical may effect the growth of an organism. Under the control conditions (no chemical), the organism grows to a mean mass of \(\mu_0 = 52.8\) grams with a standard deviation of \(\sigma_0 =14.9\) grams. These population parameters are known precisely because the organism has been grown under control conditions many many times.

    The scientist has only grown the organism under experimental conditions (with chemical) \(n=51\) times. In that sample, the masses have a mean \(\bar{x}=56.45\).

    The scientist wonders if this sample mean is significantly different from \(\mu_0\). To investigate this, the scientist will determine the \(p\)-value. The \(p\)-value represents the probability of getting a sample mean as far (or farther) from \(\mu_0\) due to chance alone.

    It is common to compare the \(p\)-value to 0.05.

    \[p\text{-value} ~=~ P\left(\big|Z\big| > \frac{\big|\bar{x}-\mu_0\big|}{\sigma_0/\sqrt{n}} \right) \]

    Determine the \(p\)-value.


    Solution


  121. Question

    A scientist is investigating whether a chemical may effect the survival rate of an organism. Under the control conditions (no chemical), the organism has a survival rate of \(p_0=0.9571\). This value is known precisely because the organism has been grown under control conditions many many times.

    The scientist has only grown the organism under experimental conditions (with chemical) \(n=70\) times. In that sample, the survival rate is \(\hat{p} = 0.9\).

    The scientist wonders if this survival rate is significantly different from \(p_0\). To investigate this, the scientist will determine the \(p\)-value. The \(p\)-value represents the probability of getting a sample proportion as far (or farther) from \(p_0\) due to chance alone. \[p\text{-value} ~=~ P\left(\big|Z\big| > \frac{\big|\hat{p}-p_0\big|}{\sqrt{\frac{p_0(1-p_0)}{n}}} \right) \]


    Solution


  122. Question

    A scientist is investigating whether a chemical may effect the survival rate of an organism. Under the control conditions (no chemical), the organism has a survival rate of \(p_0=0.0714\). This value is known precisely because the organism has been grown under control conditions many many times.

    The scientist has only grown the organism under experimental conditions (with chemical) \(n=42\) times. In that sample, the survival rate is \(\hat{p} = -0.0238\).

    The scientist wonders if this survival rate is significantly different from \(p_0\). To investigate this, the scientist will determine the \(p\)-value. The \(p\)-value represents the probability of getting a sample proportion as far (or farther) from \(p_0\) due to chance alone. \[p\text{-value} ~=~ P\left(\big|Z\big| > \frac{\big|\hat{p}-p_0\big|}{\sqrt{\frac{p_0(1-p_0)}{n}}} \right) \]


    Solution


  123. Question

    A scientist is investigating whether a chemical may effect the survival rate of an organism. Under the control conditions (no chemical), the organism has a survival rate of \(p_0=0.7778\). This value is known precisely because the organism has been grown under control conditions many many times.

    The scientist has only grown the organism under experimental conditions (with chemical) \(n=90\) times. In that sample, the survival rate is \(\hat{p} = 0.8667\).

    The scientist wonders if this survival rate is significantly different from \(p_0\). To investigate this, the scientist will determine the \(p\)-value. The \(p\)-value represents the probability of getting a sample proportion as far (or farther) from \(p_0\) due to chance alone. \[p\text{-value} ~=~ P\left(\big|Z\big| > \frac{\big|\hat{p}-p_0\big|}{\sqrt{\frac{p_0(1-p_0)}{n}}} \right) \]


    Solution


  124. Question

    A scientist is investigating whether a chemical may effect the survival rate of an organism. Under the control conditions (no chemical), the organism has a survival rate of \(p_0=0.4045\). This value is known precisely because the organism has been grown under control conditions many many times.

    The scientist has only grown the organism under experimental conditions (with chemical) \(n=89\) times. In that sample, the survival rate is \(\hat{p} = 0.2921\).

    The scientist wonders if this survival rate is significantly different from \(p_0\). To investigate this, the scientist will determine the \(p\)-value. The \(p\)-value represents the probability of getting a sample proportion as far (or farther) from \(p_0\) due to chance alone. \[p\text{-value} ~=~ P\left(\big|Z\big| > \frac{\big|\hat{p}-p_0\big|}{\sqrt{\frac{p_0(1-p_0)}{n}}} \right) \]


    Solution


  125. Question

    A scientist is investigating whether a chemical may effect the survival rate of an organism. Under the control conditions (no chemical), the organism has a survival rate of \(p_0=0.4667\). This value is known precisely because the organism has been grown under control conditions many many times.

    The scientist has only grown the organism under experimental conditions (with chemical) \(n=45\) times. In that sample, the survival rate is \(\hat{p} = 0.2889\).

    The scientist wonders if this survival rate is significantly different from \(p_0\). To investigate this, the scientist will determine the \(p\)-value. The \(p\)-value represents the probability of getting a sample proportion as far (or farther) from \(p_0\) due to chance alone. \[p\text{-value} ~=~ P\left(\big|Z\big| > \frac{\big|\hat{p}-p_0\big|}{\sqrt{\frac{p_0(1-p_0)}{n}}} \right) \]


    Solution


  126. Question

    A scientist is investigating whether a chemical may effect the survival rate of an organism. Under the control conditions (no chemical), the organism has a survival rate of \(p_0=0.0448\). This value is known precisely because the organism has been grown under control conditions many many times.

    The scientist has only grown the organism under experimental conditions (with chemical) \(n=67\) times. In that sample, the survival rate is \(\hat{p} = 0.0896\).

    The scientist wonders if this survival rate is significantly different from \(p_0\). To investigate this, the scientist will determine the \(p\)-value. The \(p\)-value represents the probability of getting a sample proportion as far (or farther) from \(p_0\) due to chance alone. \[p\text{-value} ~=~ P\left(\big|Z\big| > \frac{\big|\hat{p}-p_0\big|}{\sqrt{\frac{p_0(1-p_0)}{n}}} \right) \]


    Solution


  127. Question

    A scientist is investigating whether a chemical may effect the survival rate of an organism. Under the control conditions (no chemical), the organism has a survival rate of \(p_0=0.75\). This value is known precisely because the organism has been grown under control conditions many many times.

    The scientist has only grown the organism under experimental conditions (with chemical) \(n=24\) times. In that sample, the survival rate is \(\hat{p} = 0.9583\).

    The scientist wonders if this survival rate is significantly different from \(p_0\). To investigate this, the scientist will determine the \(p\)-value. The \(p\)-value represents the probability of getting a sample proportion as far (or farther) from \(p_0\) due to chance alone. \[p\text{-value} ~=~ P\left(\big|Z\big| > \frac{\big|\hat{p}-p_0\big|}{\sqrt{\frac{p_0(1-p_0)}{n}}} \right) \]


    Solution


  128. Question

    A scientist is investigating whether a chemical may effect the survival rate of an organism. Under the control conditions (no chemical), the organism has a survival rate of \(p_0=0.7831\). This value is known precisely because the organism has been grown under control conditions many many times.

    The scientist has only grown the organism under experimental conditions (with chemical) \(n=83\) times. In that sample, the survival rate is \(\hat{p} = 0.6988\).

    The scientist wonders if this survival rate is significantly different from \(p_0\). To investigate this, the scientist will determine the \(p\)-value. The \(p\)-value represents the probability of getting a sample proportion as far (or farther) from \(p_0\) due to chance alone. \[p\text{-value} ~=~ P\left(\big|Z\big| > \frac{\big|\hat{p}-p_0\big|}{\sqrt{\frac{p_0(1-p_0)}{n}}} \right) \]


    Solution


  129. Question

    A scientist is investigating whether a chemical may effect the survival rate of an organism. Under the control conditions (no chemical), the organism has a survival rate of \(p_0=0.4483\). This value is known precisely because the organism has been grown under control conditions many many times.

    The scientist has only grown the organism under experimental conditions (with chemical) \(n=29\) times. In that sample, the survival rate is \(\hat{p} = 0.2759\).

    The scientist wonders if this survival rate is significantly different from \(p_0\). To investigate this, the scientist will determine the \(p\)-value. The \(p\)-value represents the probability of getting a sample proportion as far (or farther) from \(p_0\) due to chance alone. \[p\text{-value} ~=~ P\left(\big|Z\big| > \frac{\big|\hat{p}-p_0\big|}{\sqrt{\frac{p_0(1-p_0)}{n}}} \right) \]


    Solution


  130. Question

    A scientist is investigating whether a chemical may effect the survival rate of an organism. Under the control conditions (no chemical), the organism has a survival rate of \(p_0=0.8202\). This value is known precisely because the organism has been grown under control conditions many many times.

    The scientist has only grown the organism under experimental conditions (with chemical) \(n=89\) times. In that sample, the survival rate is \(\hat{p} = 0.7416\).

    The scientist wonders if this survival rate is significantly different from \(p_0\). To investigate this, the scientist will determine the \(p\)-value. The \(p\)-value represents the probability of getting a sample proportion as far (or farther) from \(p_0\) due to chance alone. \[p\text{-value} ~=~ P\left(\big|Z\big| > \frac{\big|\hat{p}-p_0\big|}{\sqrt{\frac{p_0(1-p_0)}{n}}} \right) \]


    Solution


  131. Question

    A doctor runs a controlled experiment. The participants are randomly assigned to two groups: control and treatment. The participants in the control group are given a placebo. The participants in the treatment group are given a drug. After several months, each participant’s triglyceride level is measured (in mg/dL).

    x1 x2
    553.7 576.6
    577.8 633.6
    573.0 589.7
    564.3 565.6
    516.6 553.3
    536.2 531.3
    556.3 607.6
    525.2 620.1
    507.2 521.9
    601.2 585.6
    557.1 667.7
    582.9 578.0
    573.3 498.8
    519.6 641.4
    510.4 635.0
    575.8 549.0
    550.7 555.8
    585.0 596.3
    561.3 575.3
    567.5 560.8
    529.5 486.7
    584.9
    533.2
    489.7
    652.9


    You are asked to perform a two-tail two-sample Welch’s \(t\) test to determine whether there is a significant difference of means in the two samples.


    Solution


  132. Question

    A doctor runs a controlled experiment. The participants are randomly assigned to two groups: control and treatment. The participants in the control group are given a placebo. The participants in the treatment group are given a drug. After several months, each participant’s triglyceride level is measured (in mg/dL).

    x1 x2
    476.3 543.7
    589.6 539.6
    660.5 551.1
    583.9 539.1
    658.2 555.8
    658.9 528.4
    651.2 567.3
    663.5 561.9
    555.8 605.0
    513.7 582.6
    558.8 550.0
    655.6 593.0
    594.1 617.4
    565.8 592.4
    498.6 551.1
    555.9 575.8
    558.7 572.0
    699.7 538.8
    569.8 529.1
    585.4 569.7
    677.3 553.9
    594.7 593.4
    629.1
    572.3


    You are asked to perform a two-tail two-sample Welch’s \(t\) test to determine whether there is a significant difference of means in the two samples.


    Solution


  133. Question

    A doctor runs a controlled experiment. The participants are randomly assigned to two groups: control and treatment. The participants in the control group are given a placebo. The participants in the treatment group are given a drug. After several months, each participant’s triglyceride level is measured (in mg/dL).

    x1 x2
    571.3 409.4
    489.4 470.7
    475.8 543.6
    537.5 565.3
    380.0 625.8
    558.0 569.2
    553.0 479.9
    503.0 506.3
    501.9 612.4
    548.4 613.5
    555.8 505.5
    501.3 503.8
    498.8 566.0
    533.0 538.0
    437.3 529.7
    523.9 517.4
    560.2
    467.4
    498.9
    498.6
    452.3
    471.0


    You are asked to perform a two-tail two-sample Welch’s \(t\) test to determine whether there is a significant difference of means in the two samples.


    Solution


  134. Question

    A doctor runs a controlled experiment. The participants are randomly assigned to two groups: control and treatment. The participants in the control group are given a placebo. The participants in the treatment group are given a drug. After several months, each participant’s triglyceride level is measured (in mg/dL).

    x1 x2
    385.1 396.8
    408.1 400.9
    365.6 437.4
    362.8 407.9
    373.5 403.1
    404.5 397.3
    392.6 412.0
    387.0 378.2
    378.4 392.1
    398.8 409.6
    387.0 405.7
    391.3 384.0
    400.5 382.4
    378.4 381.2
    406.8 413.5
    378.3 428.8
    371.6 368.3
    394.2 425.9
    408.3
    402.0
    400.5
    384.6


    You are asked to perform a two-tail two-sample Welch’s \(t\) test to determine whether there is a significant difference of means in the two samples.


    Solution


  135. Question

    A doctor runs a controlled experiment. The participants are randomly assigned to two groups: control and treatment. The participants in the control group are given a placebo. The participants in the treatment group are given a drug. After several months, each participant’s triglyceride level is measured (in mg/dL).

    x1 x2
    405.7 435.4
    302.6 355.8
    340.7 308.0
    353.1 384.4
    393.1 369.5
    331.3 322.1
    298.7 311.8
    376.3 316.8
    348.2 345.4
    346.5 296.4
    456.2 252.8
    316.8 325.7
    401.4 327.1
    391.7 307.9
    372.6 323.6
    380.9 281.0
    297.6 329.7
    397.8 385.0
    320.6
    364.6
    318.9
    330.2
    351.7
    358.2
    324.0


    You are asked to perform a two-tail two-sample Welch’s \(t\) test to determine whether there is a significant difference of means in the two samples.


    Solution


  136. Question

    A doctor runs a controlled experiment. The participants are randomly assigned to two groups: control and treatment. The participants in the control group are given a placebo. The participants in the treatment group are given a drug. After several months, each participant’s triglyceride level is measured (in mg/dL).

    x1 x2
    562.3 578.4
    567.2 403.3
    652.4 500.2
    590.3 439.9
    512.4 504.0
    487.3 663.7
    591.6 433.2
    518.4 497.6
    525.3 488.3
    590.1 550.9
    505.8 532.7
    512.2 487.9
    568.4 394.4
    501.6 553.5
    462.7 531.6
    564.4 492.9
    514.5 520.0
    493.3 492.9
    514.5
    607.8
    587.3
    601.0
    602.7
    636.2
    579.5


    You are asked to perform a two-tail two-sample Welch’s \(t\) test to determine whether there is a significant difference of means in the two samples.


    Solution


  137. Question

    A doctor runs a controlled experiment. The participants are randomly assigned to two groups: control and treatment. The participants in the control group are given a placebo. The participants in the treatment group are given a drug. After several months, each participant’s triglyceride level is measured (in mg/dL).

    x1 x2
    323.4 305.6
    233.0 305.4
    302.9 278.7
    253.3 267.5
    317.1 332.4
    267.4 282.8
    270.4 276.2
    258.0 314.0
    290.5 284.7
    262.1 273.5
    290.1 307.0
    282.3 249.1
    280.8 308.9
    236.4 291.8
    265.6 313.5
    319.0 305.6
    311.4
    226.1
    289.4
    290.3
    320.1
    262.0
    276.3
    267.6


    You are asked to perform a two-tail two-sample Welch’s \(t\) test to determine whether there is a significant difference of means in the two samples.


    Solution


  138. Question

    A doctor runs a controlled experiment. The participants are randomly assigned to two groups: control and treatment. The participants in the control group are given a placebo. The participants in the treatment group are given a drug. After several months, each participant’s triglyceride level is measured (in mg/dL).

    x1 x2
    345.1 363.5
    304.4 340.1
    341.9 371.6
    338.0 317.8
    321.2 353.9
    346.0 337.5
    369.3 368.5
    319.8 358.1
    332.5 305.6
    313.8 344.8
    347.3 385.0
    345.9 384.1
    324.2 349.7
    324.5 362.1
    361.5 348.2
    330.1 354.7
    374.5
    404.6
    380.4
    392.3
    278.7
    362.7


    You are asked to perform a two-tail two-sample Welch’s \(t\) test to determine whether there is a significant difference of means in the two samples.


    Solution


  139. Question

    A doctor runs a controlled experiment. The participants are randomly assigned to two groups: control and treatment. The participants in the control group are given a placebo. The participants in the treatment group are given a drug. After several months, each participant’s triglyceride level is measured (in mg/dL).

    x1 x2
    258.4 257.1
    212.2 289.8
    214.7 275.6
    278.8 246.6
    248.1 275.5
    265.7 317.0
    227.2 255.6
    234.3 242.4
    214.7 197.3
    256.7 193.9
    211.5 258.8
    278.6 282.7
    223.6 218.1
    208.5 353.5
    241.6 323.0
    197.6 279.7
    221.2 246.3
    217.2 308.1
    242.1 232.9
    232.6 286.4
    210.6 229.8
    270.2 181.8
    236.9
    318.8
    251.9


    You are asked to perform a two-tail two-sample Welch’s \(t\) test to determine whether there is a significant difference of means in the two samples.


    Solution


  140. Question

    A doctor runs a controlled experiment. The participants are randomly assigned to two groups: control and treatment. The participants in the control group are given a placebo. The participants in the treatment group are given a drug. After several months, each participant’s triglyceride level is measured (in mg/dL).

    x1 x2
    340.6 200.7
    320.2 316.9
    201.7 396.0
    288.1 230.9
    228.8 202.8
    321.2 361.1
    265.2 260.9
    189.8 251.0
    266.8 300.2
    268.5 328.7
    255.1 273.7
    275.9 370.6
    297.2 253.5
    277.4 254.6
    214.2 376.8
    256.2 374.8
    287.0 235.1
    187.9
    235.6
    179.5
    249.8
    267.3


    You are asked to perform a two-tail two-sample Welch’s \(t\) test to determine whether there is a significant difference of means in the two samples.


    Solution